Cases lined with acoustic treatment are a good idea.
Not to quiet noisy parts (that won't happen)... but to help reduce/eliminate vibration related noise
 
A quiet PC is the sum of all parts.
 
High density foam would (IMO) work better than the fabric (for vibration related noise).
You won't be able to use material thick enough (inside the case) to absorb high-frequency noise.
The solution is simple.  Don't use components that make significant noise.  
 
We've thought about building custom cases.
That means a machine shop... and getting into fabrication.
Cost/time would be significant.  For most folks, not worth the expense.
 
Using large heatsinks and low-RPM fans will result in low noise.
 
Newer GTX video cards have fans that only run under heavier loads.
For DAW work, that's going to be silent.

I have read/checked out Sweetwater, your Purrrfect Audio, and lots of others sites for the silent PC options, so acoustic treatment seemed a sensible choice. Frankly, using fabric seemed a cheap/cheesy choice.
 
I certainly am not going to have a custom made case. I'd been wondering about putting the PC in a closet... "further away" from my monitoring position, as it would have to be 25+' away to go in the "next" room and that seemed more problematic than replacing/upgrading components.
When my wife and I were able to get new desktops, we bought these to start things rolling (after Chapter 7 and then recovering from that)
http://www.newegg.com/Product/Product.aspx?Item=N82E16883227593
 
I suppose a gaming case like the Versa (above) isn't that "silent DAW friendly" and is more about heat dispersion....?
Anyway, silent PC is on my list along with upgrading the mobo and RAM. I will keep the graphics card in mind, though maybe I'll just use the  "onboard" one.
Michael

pentimentosound
I'd been wondering about putting the PC in a closet... "further away" from my monitoring position, as it would have to be 25+' away to go in the "next" room and that seemed more problematic than replacing/upgrading components.

If your audio interfaces can work properly via a USB extender, then the "next" room would be cheap and most effective. all other connections (HDMI, etc) are no problem to extend.
 
FYI, I got one of these quite cases, but it wasn't quiet enough for my liking, so I was only happy after moving the PC to a separate tech room.
 
I also got an true silent all passive DAW, but that serves as all purpose PC & mobile DAW (not installed in the studio); this, however, comes at a high $$$ price (though I love that it's really not audible) ... and it creates a lot of heat ...

Jim Roseberry advised me that 15' was about as long as a usb audio cable should be. My next room is a bath, so I would have to go at least 25', unless I figure out a way to put in the hallway unobtrusively (that would be a trick, too! LOL).

FWIW, Much less hassle to just make the PC quiet.   

So I see... or should that be, hear? As in, don't want to hear!

there are easier way to make PC quiet:
1) Fractal Design Define R5 case with pre-applied "heavy" dampening (empty case weighs over 10kg)
2) Noctua NH-U14S or D15S cpu cooler, 140mm fan can go below 300rpm or even fully passive to cool down even overclocked cpu
3) get rid of all HDDs and get SSDs instead - zero noise
4) most graphics cards nowadays don't spin up their fans unless getting over 60C, and MSI Afterburner lets you tweak the fan speeds curve anyway
5) decent power supply will not spin the fan either, unless heavy loaded

<<<Fractal Design Define R5 case with pre-applied "heavy" dampening>>
 
+1 on this baby. I have two R4's and it is a great case for many reasons including space, accessibility, flexbility and quietude.

Dynamat is an adhesive backed, sound deadening product   I've used it in vehicles and household appliances to reduce unwanted noise.
 
http://www.dynamat.com/architectural-home/architectural-home-dynamat-xtreme/
 
http://www.crutchfield.com/brands/Dynamat/

The "closet" or "next room" option was going to be my next approach until I found a really quiet but stout laptop. Otherwise you could create a "sealed" area inside a studio work desk closing it off with a door and pipe vent tubes out the back or bottom or... next room.